The present embodiments relate to photon imaging. In particular, the point spread function is modeled for use with a multi-channel collimator in photon imaging.
In single photon emission computed tomography (SPECT), photons are emitted directly from radio isotopes. Similarly, in positron emission tomography (PET), positrons are emitted, which interact with electrons to form photons (e.g., gamma rays). In both cases, the photons travel through the patient's body to a detector. Prior to detection, incident photons are projected onto the detector surface with a collimator so as to allow for recovery of geometric information about the scene being imaged. The collimator has an array of bores separated by highly attenuating septa. Each bore limits the acceptance angle of incident photons at that particular region of the detector, allowing the collimator to accomplish an orthographic projection of the scene onto the detector surface. However, due to the finite length and diameter of each bore, the region of space from which photons may be admitted is not an ideal line. The region is a cone that widens with increasing distance from the entry aperture. The acceptance regions of neighboring bores overlap, imposing a blur on images projected onto the detector.
In practice, depth-dependent blur is a complicated function of imaging distance and collimator geometry and may be characterized by the distribution of radiation impinging upon the detector from a point source, also known as the Point Spread Function (PSF). A given bore has geometric entry and exit apertures limiting the angle of any lines from a point source impinging on the detector. This region on the detector is characterized by the collimator's acceptance angle, or the angle spanning the two outer rays of the cone with its vertex at the focal point within the bore. The collimator dimensions (e.g., bore length and bore width, diameter or other aperture measure) and relative detector dimensions (e.g., the distance between the back of the collimator and average location in the detector where photons are absorbed to create an image) work together to determine the acceptance angle. As the imaging depth or source distance z increases, so does the width of the region subtended by this angle. A larger area of the scene being imaged contributes to a particular detector position, increasing the amount of blurring.
By modeling the PSF as part of a system matrix in reconstruction, the reconstruction of an imaged object from detected photons accounts for the blurring. However, using the PSF based just on the ideal apertures of the bore fails to account for penetration of the collimator septa by photons, scattering within the bores of the collimator and systematic defects or tolerance shifts in the collimator.